In this paper, we consider a semi-deterministic wiretap channel where the main channel is noiseless and the eavesdropper's channel is a binary erasure channel (BEC). We provide a lower bound for the achievable secrecy rates of polar and Reed Muller codes and compare it to the second order coding rate for the semi-deterministic wiretap channel. To the best of our knowledge, this is the first work which demonstrates the secrecy performance of polar and Reed-Muller codes in short blocklengths. The results show that under a total variation secrecy metric, Reed Muller codes can achieve secrecy rates very close to the second order approximation rate. On the other hand, we observe a significant gap between the lower bound for the achievable rates of polar codes and the the second order approximation rate for short blocklengths.
翻译：在本文中,我们考虑的是一个半确定性窃听频道,主频道是无噪音的,窃听器频道是二进制消除频道(BEC ) 。 我们为极地和Reed Muller代码的可实现保密率提供了较低的界限,并将它与半确定性窃听频道的第二顺序编码率进行比较。 据我们所知,这是第一个显示极地和Reed-Muller代码在短长的保密性能的工作。 结果显示,根据全面变换保密标准,Reed Muller代码可以达到非常接近第二顺序近似率的保密率。 另一方面,我们观察到极地代码可实现率的下限与短长的第二顺序近率之间的巨大差距。
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